A recently developed class of photovoltaic (“PV”) cells and devices, sometimes referred to as “Graetzel Cells” (see, e.g., U.S. Pat. Nos. 4,684,537; 5,350,644; 5,463,057; 5,525,440; and 6,278,056 B1), is based upon dye-sensitization of a wide bandgap (“WBG”) semiconductor (i.e., Eg≧2 eV, preferably ≧3 eV), such as TiO2, for efficient injection of electrons into the conduction band upon photo-excitation of the dye molecules, followed by charge separation and photovoltage generation utilizing a liquid electrolyte for hole conduction. While such devices are attractive in terms of their inherent simplicity and use of environmentally stable WBG material, the relatively low absorption coefficients of the photodyes necessitates use of extremely thick “mesoscopic” TiO2 films for adequate capture of incident photons. Disadvantageously, however, this results in greater opportunity for loss of excited electron-hole pairs (“excitons”) due to recombination and thermalization. Consequently, the efficiency of solar conversion of such devices is generally limited to ˜10%.
According to a variation of this approach, quantum dots (“QD's”), i.e., nano-dimensioned semiconductor particles that confine the motion of conduction band electrons, valence band holes, or pairs of conduction band electrons and valence band holes (“excitons”) in all three spatial directions, are substituted for the abovementioned dye molecules (see, e.g., U.S. Pat. Nos. 6,861,722 B2 and 7,042,029 B2). Contact between porous TiO2 films and the QD's, may for example, be accomplished via absorption, utilizing a porous TiO2 body and a colloidal solution of the QD, or produced via an in situ process. PV effects have been observed with a number of semiconductor-based QD's, including InP, CdSe, CdS, and PbS. Advantages of QD's vis-à-vis dye molecules in solar PV applications involving sensitization of WBG's include better tunability of optical properties via size control of the QD particles and better heterojunction formation with solid, rather than liquid hole conductors.
As explained below, another advantageous capability of QD-sensitized PV cells is the production of quantum yields >1 by impact ionization, sometimes referred to as the “inverse Auger effect”. Since the inverse Auger effect is not possible with dye-sensitized PV cells, much higher conversion efficiencies are possible with solid state heterojunction QD-sensitized PV cells.
Referring to FIG. 1, shown therein, in schematic form, is a band diagram for solid state heterojunction QD-sensitized PV cells, wherein: CB and VB respectively indicate the conduction band and valence band energies of the QD and WBG materials (illustratively PbS and TiO2, respectively), EF represents the respective Fermi energy levels, and ΦA indicates the respective electron affinities (work functions). In order for charge injection (sensitization) from the QD to the WBG material to occur, the difference between the work function ΦA and conduction band energy CB must be greater for the WBG than for the QD.
Design rules for the materials selection process for fabricating solid state heterojunction QD-sensitized PV cells such as shown in FIG. 1 include:
1. the minimum size of the QD, i.e., Dmin=(πh)/2me*ΔEc)1/2, where me* is the effective mass of the electron, and ΔEc is the difference between the energies of the CB's of the QD and WBG materials, wherein the bandgap energy Eg of the WBG semiconductor material is ≧2.0 eV, preferably ≧3.0 eV; and the bandgap energy Eg of the QD semiconductor material is <2.0 eV, preferably <1.0 eV; and
2. the exciton radius, ax, is larger than the QD radius, where ax=εr/M*aH, wherein is the relative permittivity and M*=(Me*Mh*)/(Me*+Mh*) and Me* and Mh* denote the effective masses of the electrons and holes in units of the electron rest mass and aH is the Bohr radius of 5.29×10−11 m. The QD radius Dmin ranges from about 3 to about 15 nm, and is typically about 5-9 nm.
The term “exciton radius” ax refers to the average physical separation between the electron and hole of the electron-hole pair within the semiconductor. If the size of the semiconductor particle, i.e., QD, is less than or equal to the exciton radius, quantum confinement occurs and the energy levels in the QD are discrete and continuous energy level bands are no longer formed. Typical values of ax range between about 2 and about 20 nm.
Adverting to FIG. 2, schematically illustrated therein is a band diagram for describing the increase in photon conversion efficiency afforded by QD's, wherein enhanced photocurrent is obtained when energetic (“hot”) charge carriers (e−h+ pairs or excitons) produce a second (or even a third, etc.) e−h+ pair or exciton via impact ionization, a process which is the inverse of an Auger recombination process wherein two e−h+ pairs recombine to form a single, highly energetic e−h+ pair. In order for the inverse Auger recombination process to result in increased photon conversion efficiency, the rate at which impact ionization occurs must be greater than the rate of carrier “cooling” and other relaxation processes for hot carriers.
Referring now to FIG. 3, schematically illustrated therein is a band diagram illustrating the mechanism of operation of a solid state heterojunction QD-sensitized PV cell comprising a layer of a WBG semiconductor material (i.e., Eg≧2.0 eV, preferably ≧3.0 eV), e.g., TiO2, forming a heterojunction with a layer of a narrower bandgap QD semiconductor material (i.e., Eg<2.0 eV, preferably <1.0 eV), e.g., PbS. The latter is contacted at an opposite interface with a hole conductor, e.g., a layer of a hole conductive semiconductor material. Respective contacts (output terminals) are formed on the TiO2 and hole conductive semiconductor layers for obtaining an electrical output from the cell for supply to a load device. As shown in the figure, absorption of a photon in the QD results in formation of an energetic e−h+ pair (or exciton) in the QD, which e−h+ pair (or exciton) then produces a second e−h+ pair in the QD via impact ionization. Both excited electrons in the conduction band of the QD may then be efficiently transferred to the conduction band of the electron conductive WBG semiconductor, and thence to the negative output terminal. Hole transport occurs in the opposite direction via the valence bands of the QD and hole conductive semiconductor to the positive output terminal. FIGS. 4(A) and 4(B) schematically illustrate the directions of electron and hole travel, respectively, in the QD-sensitized PV cell of FIG. 3. As shown in FIG. 4(A), if any portion of the QD is in interfacial contact with the negative output terminal, excited electrons present in the QD may also travel directly to the negative output terminal to produce photocurrent.
Notwithstanding the potential for increased photon conversion efficiency afforded by the solid state heterojunction QD-sensitized PV cells such as described above, the heretofore utilized manufacturing techniques comprising absorption of the QD material from solution onto a porous body of a WBG semiconductor material, as well as in situ processing, result in relatively low surface-to-volume ratios of the WBG semiconductor particles (e.g., TiO2), which when combined with the relatively low coverage of the WBG particle surfaces with QD's, limits the actual performance and viability of such devices.
Accordingly, there exists a clear need for improved solid state heterojunction QD-sensitized PV cells capable of performing in optimal manner at high solar photon conversion efficiencies. Further, there exists a clear need for improved methodology for fabrication of such improved solid state heterojunction QD-sensitized PV cells in cost-effective manner utilizing readily available manufacturing instrumentalities and technologies.